You can put only but one video that shows in all pages of the song and it's translations. You can create the same effect by putting a [video:] statement within the lyrics of the song but I strongly advise against this, since this is a lyrics site and not a multimedia one and since this may generate problems in page formatting now or in the future. The link you provided has the second video within the Author's comment field.

Yes but that way, people who go straight to the translation page, which is what I usually do, will never get to see the video (not to mention the comments they're missing). That's actually a good suggestion for the site.

This example you refer to has one video in the appropriate field and one in the translation lyrics, which I do not recommend and don't like because for me it's so appalling like seeing the whole translation entered in the title field. Furthermore it presents problems to the site display formatting.
Since a song is in a different language than the translation there is no need to show the original song comments along with the translation's ones since the first would be most of the times in a different language than the one the viewer understands
If you want to enter two videos on the author's comment field you may reduce their size, so for 4:3 ratio videos a statement like

will appear side by side:

hopefully since it depends on the browser and its viewing resolution. If you lower the size of the videos you may fit more than two in one row, but this still depends on the viewer.
So please use this in the author's comment field

the author's comment field doesn't solve anything if you're not the uploader of both the lyrics and translation. you'll see the problem if you read what I wrote on my last post here ^^. I still don't understand the real issue with posting the video in the lyrics, not to mention, it's done by other mods here.